Question

In: Statistics and Probability

Use multiple regression with dummies, since the data is seasonal for the regression model. Year Sales...

Use multiple regression with dummies, since the data is seasonal for the regression model.

Year Sales (Millions) Trend
2014 1 480.0 1
2014 Q2 864.0 2
2014 Q3 942.0 3
2014 Q4 1,100.0 4
2015 Q1 1,200.0 5
2015 Q2 1,900.0 6
2015 Q3 1,900.0 7
2015 Q4 1,300.0 8
2016 Q1 1,200.0 9
2016 Q2 1,500.0 10
2016 Q3 1,200.0 11
2016 Q4 500.0 12
2017 Q1 356.0 13
2017 Q2 1,300.0 14
2017 Q3 1,000.0 15
2017 Q4 425.0 16
2018 Q1 273.0 17
2018 Q2 769.0 18
2018 Q3 456.0 19
2018 Q4 387.0 20
2019 Q1 245.0 21
2019 Q2 882.0 22
2019 Q3 557.0 23
2019 Q4 551.0 24

Solutions

Expert Solution

Result:

Dummy variable is created .

Q1= 1 if it Quarter1 or 0 therwise

Q2= 1 if it Quarter2 or 0 therwise

Q3= 1 if it Quarter3 or 0 therwise

Regression Analysis

R²

0.511

Adjusted R²

0.408

n

24

R

0.715

k

4

Std. Error of Estimate

372.640

Dep. Var.

Sales (Millions)

Regression output

confidence interval

variables

coefficients

std. error

   t (df=19)

p-value

95% lower

95% upper

Intercept

a =

1,218.475

217.817

5.594

2.15E-05

762.580

1,674.370

t

b1 =

-36.284

11.135

-3.259

.0041

-59.589

-12.979

Q1

b2 =

-193.685

217.722

-0.890

.3848

-649.382

262.012

Q2

b3 =

419.432

216.293

1.939

.0675

-33.275

872.139

Q3

b4 =

262.383

215.432

1.218

.2382

-188.521

713.287

ANOVA table

Source

SS

df

MS

F

p-value

Regression

2,757,980.081

4  

689,495.020

4.97

.0065

Residual

2,638,352.877

19  

138,860.678

Total

5,396,332.958

23  

The estimated regression line is

Sales = 1,218.475-36.284*t -193.685*Q1+419.432*Q2+262.383*Q3

51.1% of variance in sales is explained by the model. F=4.97, P=0.0065, The model is significant.

Data:

Year

Sales (Millions)

t

Q1

Q2

Q3

2014 Q1

480

1

1

0

0

2014 Q2

864

2

0

1

0

2014 Q3

942

3

0

0

1

2014 Q4

1,100.00

4

0

0

0

2015 Q1

1,200.00

5

1

0

0

2015 Q2

1,900.00

6

0

1

0

2015 Q3

1,900.00

7

0

0

1

2015 Q4

1,300.00

8

0

0

0

2016 Q1

1,200.00

9

1

0

0

2016 Q2

1,500.00

10

0

1

0

2016 Q3

1,200.00

11

0

0

1

2016 Q4

500

12

0

0

0

2017 Q1

356

13

1

0

0

2017 Q2

1,300.00

14

0

1

0

2017 Q3

1,000.00

15

0

0

1

2017 Q4

425

16

0

0

0

2018 Q1

273

17

1

0

0

2018 Q2

769

18

0

1

0

2018 Q3

456

19

0

0

1

2018 Q4

387

20

0

0

0

2019 Q1

245

21

1

0

0

2019 Q2

882

22

0

1

0

2019 Q3

557

23

0
orchestra answered 1 year ago
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